One small thing happens, causing something else to happen, causing something else to happen, causing something else to happen, and so on until after all of that, something (usually quite trivial, like turning on a shower) happens. The joke is that it would have been easier to just turn on the shower than set it all up. Essentially it's a Zany Scheme performed by a machine. As with the Unspoken Plan, the efficacy of a planned contraption is generally inversely proportional to the amount of its workings known to the audience. You can read more under Rube-Goldberg Machine on That Other Wiki.